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Cauldrons are items in the form of large pots that witches use to make potions. These items contain the magical energies resulting from the brew and the chemicals used to create it. These magical energies can seep into the cauldron over the course of numerous generations. As the pots absorb the runoff of numerous potions being brewed in them, they ultimately become magical themselves. This makes the potions made within them more powerful and potent, with the cauldron adding its own power to the contents of the brew. This makes the oldest cauldrons incredibly valuable to witches, with these items being passed down to each generation over hundreds of years through a coven.

Newer cauldrons lack the history and usage of these ancient cauldrons, and lack the slow buildup of magic that their counterparts have developed over the centuries. As such, they are just normal pots used as containers for brewing potions. However, potions that are made within recently built cauldrons brew faster, making the process of potion making quicker. This has led to a competing market where cauldrons can be bought and sold, dependent on the potential needs of an individual. However, the situation seems counter-intuitive. If older cauldrons have built up magic over many centuries, it stands to reason that brewing potions within them would speed up the process and make it more powerful, with the cauldron adding its own magic to the potion and maxing it up. As it turns out, a cauldron that isn't magical at all due to its recentness is more likely to win out in this regard. How can this be the case?

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  • $\begingroup$ With a catalyst. $\endgroup$ Jul 8, 2021 at 18:32

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Cross-contamination

"As the pots absorb the runoff of numerous potions being brewed in them..." sounds like a contamination problem with old potion residue working at cross-purposes to each other. One could never quite get all the residue gone using historical cleaning techniques because of the magical nature of potions and so back then witches actually had to be quite careful about the order in which they brewed potions in; imagine brewing a curse potion and then a love potion in the same cauldron back-to-back, oof. (Some especially skilled witches used these contamination effects to put extra twists into their potions but it was always a dicey business. Nowadays, that would never get past the FDA, EMA, or other local modern regulatory agencies regulating the brewing of potions for human, etc. consumption.)

Brewing in a clean cauldron does not benefit from leftover magical energy stored in the cauldron but also does not suffer from accumulated potion residue interfering with the current potion being brewed, making the brewing process quicker and less finicky. Optimally one would only use each cauldron only for a specific type of potion to get the best of both worlds but that is too expensive outside of industrial scale witchcraft facilities.

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    $\begingroup$ It explains why witches specialized. $\endgroup$
    – Mary
    Jul 6, 2021 at 17:15
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    $\begingroup$ Building on this, perhaps brewing a potion in a "cross-contaminated" cauldron requires modification/recalibration of the ingredients or process. Perhaps a potion that would normally only require goat's blood and eye-of-newt now requires a pinch of salt to neutralize the amorific residues of last week's run of love potions. Oh, and perhaps less goat's blood than usual because we did use goat's blood in several other recipes recently. And of course we'll need to keep the fire lower than called for...this cauldron's been running a little hot ever since that batch of Alchemist's Fire... $\endgroup$
    – Qami
    Jul 6, 2021 at 17:46
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    $\begingroup$ Would this lead to a pot for restoratives and a different pot for poisons, etc. Then the pot would "remember" how to make this thing again, faster, stronger, and more efficiently? Your market would be used pots for specific brews, or brew families. $\endgroup$
    – Jammin4CO
    Jul 6, 2021 at 17:52
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    $\begingroup$ This also means that there are different types of old cauldrons. Some used exclusively for benefitial potions, some only for harmful ones. A good (and somewhat affluent) which always has these two, no matter their age $\endgroup$
    – Hobbamok
    Jul 7, 2021 at 7:58
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    $\begingroup$ Re: multiple cauldrons, it depends on the scenario. Assuming that it's the common Ye Olde Medieval Fantasie Worlde, the likely financial situation is that your average practitioner could only afford a single cauldron since they're expensive to handcraft and so they would have to use their experience and skill to adjust the brewing process on-the-fly to get the right result. Perhaps a very successful witch doing lots of business in a major city of the time could afford more than one cauldron but it certainly wouldn't be many. $\endgroup$ Jul 7, 2021 at 15:51
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Power is proportional to brewing time, but only to the capacity of the cauldron.

It's not that a newer cauldron can make the same potion faster, it can make a weaker potion faster. This is because a cauldron imbues magical power the longer you cook the brew, but only up to a certain point. In a new cauldron with little magical energy, you may exhaust the magic after brewing for just a few minutes - continued preparation time won't make the brew any stronger. In a very old and powerful cauldron, however, one can brew the potion for days on end and have it increase in power the whole time. But while both cauldrons are in their functional time period, magic is imbued at the same rate - at the end of a few minutes' brew, both the new and old cauldrons produce identical results.

A witch could use an old cauldron to brew a weak potion very quickly, but that's a complete waste of an old cauldron, as old cauldrons are the only thing you can use to make a strong potion. It's not that old cauldrons can't brew things quickly, it's that they're usually reserved for things that take longer to brew. Newer cauldrons prepare potions more quickly, but the product is inferior - you can brew a weak potion in a new cauldron quickly, or a more powerful version in a old cauldron at the cost of more time.

In a way, it's analogous to why you wouldn't age a crappy wine for a short period of time in a fine oak barrel - it's a poor use of a good barrel. If you observe that wines aged for a short period of time are aged in "bad" barrels, you might suspect that bad barrels age wine faster, but the true reasoning is that you wouldn't use a good barrel to age something for a short period of time in the first place. The choice of barrel doesn't change the aging time, but the aging time informs the choice of barrel. Similarly, a new cauldron doesn't brew potions faster, but you would only ever make a fast-brewing potion in a new cauldron and not an old one, since the old cauldron has better uses.

As an additional bonus, using the new cauldron makes it more powerful. The per-use cauldron improvement from brewing a potion may diminish over time, so as cauldrons get more powerful, it becomes more difficult to make them even more powerful. Brewing 10 potions each in a brand new cauldron will imbue more total power than brewing 10 potions in one old cauldron, further bolstering the reason why you'd want to use a new cauldron for non-complex, quick-brewing recipes.

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Technological advances

Just because magic is involved, doesn't mean that technology can't play a part. In particular, advances in materials might make a superior cauldron. Traditionally cauldrons were made of cast iron, but iron has magic-inhibiting properties; fancy new cauldrons made of aluminum doesn't have that problem. Aluminum itself isn't new of course, but until recently it was cost prohibitive to make something as large as a cauldron from it. Further advances are being made by the witch-tech industry, experimenting with alloys incorporating silver and gold that further enhances the circulation of magic within the pot.

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    $\begingroup$ I like the use of aluminum instead of iron alloys. I am curious how well copper will work. $\endgroup$ Jul 7, 2021 at 13:03
  • $\begingroup$ Copper and aluminium could both be a health hazard. $\endgroup$
    – Michael
    Jul 7, 2021 at 13:15
  • $\begingroup$ Aluminum makes a lot of sense if the quality of the cauldron somehow depends on electrical conductivity. Then the best would be gold, then silver, copper, aluminum, with iron a ways behind. Gold and silver would be very expensive, and aluminum (as in our world) becoming dramatically cheaper would increase its usage so that it could become comparable in price to iron with much better conductivity. $\endgroup$ Jul 9, 2021 at 4:28
  • $\begingroup$ Teflon coating for easy cleaning between batches? $\endgroup$ Jul 9, 2021 at 14:14
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Ever wonder why really strong potions take so many more ingredients?

It is because the brewer has to compensate for the residue from previous brewings. The older the pot, the more balancing has to take place. This requires a very experienced practitioner. But the results are worth it! The additional ingredients, potion complexity and layers, as well as the residual magic and added brewer focus produce the very best results. Anybody can brew a love potion in a new pot. And most can brew about anything in their own pot because they know the history. Those who pass on the tradition and pot genealogy through family lines can produce remarkable results. But only the truly practiced can react on the fly to unexpected changes that can occur while brewing in an old and unfamiliar pot. And even fewer will have the necessary ingredients on hand to supply such variety as may be required. There are hallowed tales of times when several brewers joined together, each with their own knowledge and ingredients to, on rare and special occasions, produce magic potions of legendary power.

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The magic messes up the reaction speed of the ingredients

The cauldron is basically an environment where a group of reagents are kept, at peculiar ratios and providing some external energy (the fire below), in order to mix and create a suitable potion.
Of course, not all the reagents will be able to combine: even if their stoichiometric ratios are 100% precise, you will hardly have a 100% outcome, because not all the reagents will have the chance to come to contact and have the chemical reaction. This process usually follows an exponential decay: at the beginning there are a lot of unreacted ingredients, so their combination is very fast, but after a while, the density of the ingredients decreases, so they take longer to react.

Without magic, the process is straightforward: add ingredients, light the fire, and after two hours, the majority of the ingredients will react and create a potion.
Because of the exponential nature of the reaction, keeping the potion in the cauldron longer would be a diminishing return: after 4 hour, a smaller quantity of the remaining ingredients will react, so that your potion will be - say - only one tenth stronger, rather than two times stronger.

But if the cauldron retained some magic, this is no longer the case: the magic (somehow acting like Maxwell's demon, slowing down the reaction at first, then keeping it going later) will modify the reaction speed making it linear, so that if after 2 hours the potion will be weaker (less ingredients have been able to react with respect to the "muggle" cauldron), after 2 hours it will be twice stronger, and so on till the complete transformation of all the ingredients.

Basically, the cauldron without magic could in reality provide a potion of the same strenght as the magic one (once all the ingredients have been able to react), but this would be possible only in a timespan of some weeks, while the magical cauldron could give the maximum powered potion after one day. But if you want a lesser potion, the first cauldron will provide it faster than the magic one.

Of course in such scenario, the difference between a weaker potion (enough ingredients have reacted) and a strong potion (all ingredients have reacted) would be in the order of 70% vs 100%, so not a very strong one.

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Pots are like barrels for wine.

Old pots store the magic of the previous brews and slowly seep it out into to potion you are currently making. If you know what you are doing and the history of the pot, then you can use that to infuse and strengthen your potions with all kinds of funky, "fermented" attributes that newer pots simply lack.

Newer pots however do not fight you along the way. You do not have to clean and decurse them. Emotions like love or lust can't seep into the newt-potion (unless you want to, of course). No memories from old victim's hair, no accidental love-hate potion. You do not need antidotes for that kind of stuff, because the pot had no time to accumulate them yet. And no antidotes, no cleaning and no decursing means fewer steps in the brewing, so less time spent. It's just cleaner and faster.

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  • $\begingroup$ This is why there is a cross Atlantic trade in whisky barrels. American whisky is always made in new barrels, whilst scots whisky can be made in used barrels, so these days is usually made in barrels that spent their first cycle aging American whisky. $\endgroup$ Jul 9, 2021 at 16:59
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When reading your question I immediately thought of something else. Your question would be similarly valid if you changed "cauldron" to "cast-iron skillet" and "potion" to "cornbread". I'll answer in terms of a cooking analogy both because I think the same logic applies and because now you've made me hungry.

My family has a cast-iron skillet that we inherited from my grandmother. It has seen over 60 years' worth of use. It's well-seasoned, and even pre-boxed cornbread mix comes out fluffy and delicious. I absolutely love that thing, I swear it must be magical by now.

A while back, I found this new thing at the grocery store. It's a little plastic cup that you add water to the contents, microwave for a couple of minutes, and you end up with a single-serving cornbread muffin.

The newfangled instant cornbread is an order of magnitude faster than using the skillet. The results, however, are much drier than the skillet version, the texture is spongy instead of crumbly, and the flavor lacks all the subtle nuances that I'm accustomed to. Some people don't really care about any of that or can't taste the difference and just want some cornbread without a lot of fuss. If that's you, then you'll probably be fine with the instant option. If you want the type of rich flavor that you can enjoy by itself or as an ingredient in other dishes, then you really need to pull out the skillet and make it the traditional way.

Your cauldrons are no different. Newer cauldrons might make potions faster, but there's a lot more to the process than speed alone. A hastily brewed potion will give you the general effect that you're going for, but anyone who has experienced real, traditionally-made potions will tell you that it's not really the same. You get so much more out of using the traditional methods and a well-seasoned cauldron. Sometimes you want the highest-quality potion you can make, and other times you just need something quickly that more or less gets the job done. Different tools for different situations.

It's up to you what potion quality might mean in your world. There are lots of knobs you can turn: effect duration, potency, yield, amount or severity of side effects, shelf life, suitability for use as a reagent, aftertaste, ingredient type/quantity, etc.

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If you have ever tried to beat the egg whites, you know that any trace of oil/fat in the container will make the task impossible: it needs to be clean and fat free.

Or have you ever drank water from a glass where there was some beer or wine? You will still taste/smell the beer/wine.

Something similar happens with these cauldrons. For some specific usage, a new, clean one is much better or there is no alternative at all to it in order to achieve the desired result.

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New Cauldrons=Better Conduits

Cauldrons are used to brew potions because they are made of metal, which is a natural conductor of electricity, heat, and magic. Thus, when one is brewing a potion in a cauldron, the reaction between metal and cauldron causes the potion to become magical, to gain the charge necessary to be more than just a funky broth.

The cauldron is essentially acting as a circuit, transferring magical power from itself to the potion, and new cauldrons harness the released energy of the potion brewing inside it as well, making the potion ready faster while also increasing potency. Thus, for maximum speed and potency (with minimal fuss), an absolutely fresh cauldron is best.

Older cauldrons retain traces of the magic that's gone through them, much like how certain metal cookware will develop patina, which influences the potion and makes it takes longer to brew. However, since the cauldron is adding to the magic of the potion, not just transferring magic from somewhere else (the wand stirring the potion, the magic fire heating it, etc.) to the potion, a beautiful synergy results that makes stronger potions. However, these potions are certain to have additional effects, to go beyond the limits of a normal potion's effect, which can be problematic.

Cauldrons made with newfangled 'stainless' metals act like fresh cauldrons and can never gain the synergical effects of an older cauldron, but brew potions faster and cleaner, while older, conventional cauldrons make stronger potions with extra effects.

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Different materials have different "magical indexes"

Traditionally cauldrons were cast of relatively pure iron. Due to it's nature, these cauldrons were most absorptive and transformative of the magic contained in potions brewed within. Newer techniques in metal working have allowed the creation of wrought iron (note I mean the alloy here, not worked iron) and steel cauldrons. These alloys reduce the absorptive and transformative effects upon the potions, resulting in faster brew times, but less potent potions.

Note that in this model well used iron cauldrons do "cook" faster after they've been properly seasoned, if a harmonious potion is being brewed within them, but the first brew will probably take WAY longer than usual. A steel cauldron on the other hand will brew fast on the first brew, because it absorbs very little of the magic of the potion, but also because of this never gains much in the way of harmonious enhancement for future brews. Wrought iron cauldrons on the other hand offer a nice compromise, though they do tend to lose their magical attunement if they aren't used for a while.

Many witches will have 3 cauldrons, a large iron cauldron for important brews (due to the length of time required these are in near constant use), a medium size wrought iron one for seasonal or large batch brews (300 sleeping droughts to put a whole castle to sleep), and a small steel one for rush jobs.

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Powerful magic doesn't just build up like water filling a barrel — if it did, it would eventually overflow the cauldron, and they would reach an upper limit. Instead, it also "thickens" into a denser form, resulting in a lower flux — so it takes longer to seep into the potion. This is why experienced magic users will tell you that it "feels heavier" or "more sluggish", and takes longer to get going. (But is equally hard to stop once it does, well worth the wait!)

As a non-magical equivalent, using a new cauldron with "unseasoned" magic is like pouring sugar-water into a bowl. Using an old cauldron with potent magic is like pouring molasses/treacle. The most ancient and revered cauldrons are like trying to pour pitch.

There are, of course, ways to speed up the transfer — equivalent to warming the molasses or pitch — but you have to be careful that this doesn't ruin the other requirements for the potion.

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In ancient times, potions were developed mostly by trial and error, based on known properties of several key ingredients. Why, exactly, a potion might require slow stirring, fast stirring, or no stirring at all; or several reheatings at carefully measured intervals; a large flame, or several smaller flames; and so on, was not understood. An experienced Potion Master would know what alterations to try and what could be reasonably expected to happen, and the same potion could be brewed in a dozen different ways, leading to stronger or weaker brews, slower or faster completion, or even saving on some specific expensive ingredients.

With the flourishing of the modern Potions science, careful experimentation led to the concept of "critical volume" - in any brewing, at the culmination point, there is a volume inside the total potion mass where the raw ingredients blend and absorb the mana from the enchantments, the cauldron itself, and the innate ingredient qualities. This volume is defined by precise conditions of pressure, density, viscosity, and temperature (which is why some potions can't be brewed at all in cauldrons too small or too large).

Immediately after the culmination point, the activated potion dilutes in the total potion mass, resulting in what is actually an inferior brew. The critical to total volume ratio is the brewing efficiency of the process, which depends on the wizard's ability, the cauldron's potency, as well as the cauldron's physical properties. And here finally is where modern metallurgy comes into play: a modern cauldron allows a better thermal stability, and a larger volume where the critical conditions are fully attained together; so, while the cauldron potency is less, the increased brewing efficiency more than compensates for this loss.

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The material of new cauldrons acts as catalyst that speeds up chemical processes in brewing. In process of brewing this catalyst leaks into potions, but on other hand particles responsible for magic replace them. Thus the effectiveness of catalysation process slows down as cauldron is used more and more, but magic stored in cauldron starts to build up.

Or maybe there is some polymerization process that locks up magic in catalyst thus changing the cauldron and allowing more efficient build up of magic in process, but the catalyst isn't as effective anymore.

Now why some industrious brewer hasn't thought of just adding tiny shavings of new cauldrons to mix every time? Maybe if the concentration in potion is too high it becomes harmful. Or the catalyst would stay effective after brewing process thus resulting spoilage potion as it over develops.

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  • $\begingroup$ Welcome to worldbuilding Ekaros. We invite you to take pour tour and read-up in the help center about our ways, enjoy the site. $\endgroup$ Jul 7, 2021 at 13:36
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Old cauldrons are too heavy / rough for modern induction stovetops, and the stored magic can interfere with the induction. A newer cauldron on a modern induction stovetop can be brought to a boil faster than an old cauldron, even on gas.

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  • $\begingroup$ This was exactly what I was thinking. Super simple. Magic blocks heat induction, so magic cauldrons take longer to reach proper temperatures. The more magic, the longer the heating process. $\endgroup$ Jul 9, 2021 at 0:25
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Grill vs. slow cooking

Simple thinks may work fast but for best result usually are needed much more complicated ways.

You can put pice of meat on grill and be done with it in a minute. Some may like that, but it is nearly charcoiled on outer and nearly raw in middle and all spice is just on top of it. If you put the same meat to marinade, then cook it in big ceramic pot on low heat for hours, then the meat is cooked equally inside and outside, the taste of spices had reached its insides too and the meat is totally different after the whole process.

Now think about Potion of Love - if you are desperate with no time and skill, sometimes even technical ethanol+some watter may bring some temporary results (or not), but good old wine and candles are usually better and combination of strong alcoholic drinks, juices, fruits in combination with sunset, nice weather, soft music and sea may work even better and last for full night, but it is still nothing in comparation with true Potion of Love, that work for whole life. But sometimes just the technical ethanol+some watter is good enought.

But cooking Potion of Love by putting some kind of igredient to a cup and microwave it for few minutes, until it boils may bring something - probably something with terible chemical result and way more side effects, than the desired result. Why it is so is simple - there is no magic, no work, no fire element, no internal resonation - just some fool chemistry.

For true magical Potion you need those ingredient carefully selected, deep magical background and both knowledge and practice of the witch and it had to be boiled in cauldron on a real and life fire (which adds its natural magic too) for sufficiently long time, so all the mixing and timed adding of ingrediets can create something magical. (Automatization would not work for obvious magical reasons)

Now if you have old cauldron, which was used this way many times over the years, all the magic around it would soaked in and slowly transform it to actually magical item. Using the same approach would fix in and helps to harmonise the process of magical transfer according it user personality - so it is also the reason, why cauldons are usually inherited by child of the original owner (or somebody else, who helped for years with working the cauldron, is accustomed to the style and the cauldron is already harmonised whit her/him).

Fire magic if fierce and fast and the cauldron is one of way to tame it and use it more consistent and harmonised way inside the potions. Old cauldrons are especially good at it, as they are trained by generations of witches to do so. So they feel a lot heavier then their weight really is and they resist to fierce fire and accumulate its power to slowly transfer it inside in harmonised way, where the "tamed" fire power oscilates in the whole potions consistently, taking the best out of ingredients and trasforming it really strong and elaborated potion. But it taks a lot of time to hamonise all those flowers, eyes, liquides, fire, will and magic. So the potion is in the end really well prepared, but it takes way longer until it even start boiling, not mentioned until the fire magic is fully and flawlessly merged inside.

On the other hand new caulron is not much more, that metalic pot, which simply distributes the fire power somehow around its content, not caring how. It is also the reason, why new cauldrons are more prone to singe some ingredients, if not constantly stirred. Old pots prevents that usually.

That results to new pots to transfer the heat and the magic of fire inside a way faster, but also a way less coordinated and effective way. With good skill, lot of stirring and some practice you can make a potion in it faster, but it would not be so harmonical, potent and elaborated, as is possible to get from old, trainded cauldron.

Many times it is still "good enought", sometimes the time is even so crucial factor, that you accept all other problems and sideeffects, like when you are making a lot of healing potions for already wounded fighters in war.

If you are making Potion of Love just for trade, it is ok, if it would "works for any two, who will drink it together from one cup" and over years affected man would lose some more hairs and woman get some more weight, so new cauldron fits well.

But if you want to make Potion of Love to bind specifically princess Eleanora to prince Fernando and nobody else, then there is no place for "any two" or some sideffects, so the choise is straighforward ...

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Consider the iron core of a transformer. It itself cannot generate a magnetic field, but it can channel a magnetic field and it can become magnetized.

What I'm about to say isn't true, but sounds good enough to maybe be true:

If the iron core isn't magnetized, then there is no pre-existing field to compete with the applied magnetic field. When you apply an external magnetic field, with no competition, the magnetic field flows faster but you're limited to the applied field itself.

With age, the iron core becomes magnetized. Its field will now compete with applied fields, which limits the rate of change of the applied magnetic field, like an inductor. This means it takes longer for the applied field to come up to full strength, but when it does you have the combined fields of the applied external field and the magnetized iron core's field.

Again, not true at all, but sounds passable.

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A new cauldron can absorb more excess magic

Before a potion is considered complete, the chemicals and magic within them have to stabilize and reach equilibrium, so that the magic from one ingredient does not overpower another. During this stabilizing time, some excess magic is produced as ingredients react with each other. This adds some instability and causes the brew to take longer to reach equilibrium.

A new cauldron, being effectively a blank slate, absorbs some of this excess magic before it can react with any of the ingredients. This makes it stabilize faster, but also slightly weakens the resulting potion. An old cauldron doesn't absorb a lot of magic, and compounds the problem by adding and mixing some old magic back into the potion. This causes more instability, which takes longer to go away, but results in a stronger potion in the end.

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The cauldron's material is like a magic vacuum. Also magic-absorbed material can be affected by magic to be made more potent.

The substance cauldrons are made out of is special. It is like a magic vacuum. It wants to be filled. Magic is practically drawn to it. If a brand new cauldron is filled with a bit of magic it wakes up and magic is drawn in explosively, but invisibly. You can't tell by looking at it how much magic is rushing in, but it is. The universe is trying to equalize between a reality brimming with magic and a magic-substance devoid of it (which all newly-made magic substances are.)

This lets potions go bad if not properly contained, the magic leaks out of them as a potion is nothing more than concentrated magic. It will slowly evaporate from the liquid if left to itself. If it's in the cauldron it will leak out into the world, but the cauldron having been in contact will have been acted on. Like a sponge it takes in magic, but doesn't release 100% of it. That extra bit doesn't just fill up pores of the cauldron, but changes the magical makeup of the substance itself.

Once tiny amounts of the cauldron are magic-filled-substance then less of it is magic-devoid. The pull of the vacuum isn't as strong as the last time, because it's more magical and less magic-devoid.

At first you'd think there would be an end to this at some point, once the cauldron's substance is entirely magic-filled that's the end of it. It can't become more potent. Well it can't brew potions any slower, that's for sure, but magic will still impart its effects on magic-filled substances too. This provides a lower bound for brewing speed, but no upper bound for brewing potency.

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Pressure cooker!

The technology advance brings us gastight cauldrons that can be boiled at higher temperatures.

The high pressure poses some dangers as well.

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Potent magic comes from rich stories

If you pluck a hair from the chin of an orphan and add it to swamp water collected at midnight, throw in an inch of root of an ancient tree from a graveyard, and very slowly bring it to a boil while constantly sprinkling in powdered emeralds, then leave it to simmer for 8 days.... well, why does it take 8 days?

The answer is partly due to physical realities, like needing to soften and soak the root so its essence can dissolve in the water, but is also very much due to each ingredient needing to tell its story. The hair tells the story of a life of challenges; the root tells the story of all the people it has outlasted, the emeralds tell the story of millions of years of formation. The more complex the story, the longer it takes to "tell". That is why ingredients with unique origins yield more powerful magic. And need more brewing time.

Cauldrons hear countless stories from the ingredients that are put in them, and they retell these stories as each new potion brews. Not that these stories are told using words, or that ingredients and cauldrons have minds of their own—but just as the people we interact with slowly become part of us, and change us, so too do the mingling ingredients slowly take on a collective identity.

So, basically, old cauldrons take a lot more time to tell their stories, and this means it takes longer for a potion's ingredients to properly tell their own stories. Ultimately the potion ingredients are what determines what the potion can do, so if there isn't enough time for their history to become part of the potion, the potion will be useless. On the other hand, a cheap cauldron and cheap ingredients will be ready much more quickly, but the potion will be far less potent because it has very little character.

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Old magic also adds contamination that has to be purified.

A old cauldron can make more powerful brews but the brews also take longer because the cauldrons magic contaminates the magic of the ingredients with echoes of past potions, these echoes need to be purified/processed out. which adds extra steps.

A new cauldron has no magic to add, so there is less magic in the potion, but it that also means the potion does not need to be purified of contaminating magic so the process is a lot faster.

this does mean an old cauldron that has only ever been used for brewing one specific potion would be both powerful and fast, but you could say the echoes are too erratic so they still need to be purified out.

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Magic is an insulator

Old cauldrons soak in the magic. Magic they bleed back into the potions. This is good.

But magic also resists heat. This is bad. The pot heats of more slowly, so the potion cooks more slowly. Also, the magic distribution in the metal is uneven, so while one section of the pot is 100 degrees C, 5 cms away, the metal is only 90 degrees. This effects the cooking speed, and also means you need to stir it more to keep the temperature of the mixture even. Toil and Trouble indeed.

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